The h Bar

Slereah

7:00 PM

@ACuriousMind I ask you

0celo7

I'm an engineer, I dunno anything

Slereah

Or @Danu

Since you're actually here

John Rennie

@barrycarter: I'm around for the next half hour or so if you want to ask anything ...

0celo7

@Slereah Wait what

What rule

Slereah

10 mins ago, by Slereah

Should I do $d^n p \rightarrow -d^n p$ if n is odd

This thing

barrycarter

7:03 PM

@JohnRennie Awesome! OK, I want to use the line invariant to compute position for a constantly accelerating reference frame.

Danu

So all it took was someone who really wanted SRT answer to make you a regular in this chatroom @JohnRennie?

barrycarter

I summoned him. It's a Level 4 Spell.

"Summon the Rennie"

Danu

Line element, or invariant interval ;)

barrycarter

The thingy @JohnRennie showed me yesterday.

Danu

Damn I messed that up :P

barrycarter

7:04 PM

I don't expect much from you, @Danu

John Rennie

@Danu the chat room has got a lot more interesting in the last few weeks. Last night I spectated at an argument between Barry and 0celo7 about manifolds and actually learned something.

barrycarter

@JohnRennie Really?

0celo7

@Slereah It's $-$ for odd, $+$ for even.

I think $\int d^np$ is $+$ $\forall n$.

John Rennie

Yes, the formal definition of a chart and it's relevance to coordinates was new to me

0celo7

@JohnRennie ...How.

Slereah

7:06 PM

Sounds about right

John Rennie

But you kind of lost me after that

0celo7

How can you know 100,000 rep worth of GR and not know the formal definition of a manifold??

barrycarter

@JohnRennie Ah, but probably not useful. OK, if I see an object accelerating constantly, in 'du' time for me, the objects 'dx' is v[u]*du + (an acceleration term). Good so far?

John Rennie

@0celo7 you have to understand that my background is as an experimental colloid scientist. I knew absolutely nothing about GR until I joined the Physics SE.

0celo7

@JohnRennie Yeah, but you've never read the classics? MTW, Wald, HE?

John Rennie

7:07 PM

And even now my fundamental knowledge of maths is appallingly bad

Have you ever tried reading MTW?

Danu

Are you interested in changing that, or not really?

barrycarter

Don't iconoclastify yourself!

0celo7

@JohnRennie A section here and there.

@JohnRennie We can help you.

John Rennie

Me too. For example I read chapter 6 to learn about accelerated motion in SR - which his Barryness is about to benefit from :-)

But as a whole it's utterly indigestible

barrycarter

I dub thee Sir @JohnRennie

0celo7

7:08 PM

@JohnRennie Let me see.

Let's get out the legal copy

Danu

Carroll is the only real GR book :3

0celo7

@Danu Leave.

John Rennie

@Danu to be honest I like playing in the shallow waters of GR

0celo7

eye twitch

@JohnRennie What part in MTW is confusing you

John Rennie

It would be nice to be able to swin down into the deep water, but I doubt I have the concebntration to learn that much maths these days

Danu

7:10 PM

@JohnRennie Carroll :3

0celo7

Don't listen to him @JohnRennie

Read Sachs and Wu

Danu

Bad notation, bad remarks about the nature of mathematics and physics ;)

Slereah

Phew, momentum proven

barrycarter

Physicists seem to place great stock in books.

@JohnRennie Since I get distracted easily, I won't fault you, but let me know when you're ready.

0celo7

@Danu Also they require you to be familiar with Riemannian geometry before reading it

3

A: Getting started self-studying general relativity

This list is extensive, but not exhaustive. Special Relativity E. Gourgoulhon (2013), Special Relativity in General Frames. This is a rigorous and encyclopedic treatment of special relativity. It contains pretty much everything you will ever need in special relativity, like the Lorentz fac...

John Rennie

7:11 PM

@0celo7 Take chapter 6: they could have said "we're looking for a metric where the norm of the four-acceleration is $a$ and here's how we do it"

0celo7

@JohnRennie I have a nice list

Right there

For you to look at

John Rennie

Instead they assume that's obvious - but it isn't

0celo7

@JohnRennie What page

John Rennie

Anyway @barrycarter what did you want to know?

0celo7

Because that doesn't make much sense to me

What four-velocity

And why would they call that $a$

Very confusing

John Rennie

7:12 PM

Oops, I meant four-acceleration

0celo7

...of what?

barrycarter

@JohnRennie Oh, if an object has constant acceleration in its own frame, my observation of its motion in du time is v[u]*du + (some acceleration term), right?

John Rennie

of the observer at the origin

@barrycarter it's a surprisingly involved calculation

0celo7

@JohnRennie why don't you want to learn some math :(

barrycarter

@JohnRennie Well, I see the acceleration term as a t dt but notice I actually mean t not u. The acceleration is constant inthe other frame.

Danu

7:14 PM

@barrycarter Objects do not accelerate in their own frame

barrycarter

@Danu You know what I mean :P

Danu

No, I don't really...

John Rennie

One way is to note that in the Earth frame the acceleration of a moving observer is a/gamma^3, where a is the acceleration measured by the accelerating observer

0celo7

According to MTW that's not true @Danu

barrycarter

@Danu Meaning that the change in velocity for a third party observer is based on the object's frame.

3075

7:16 PM

hi

Danu

@0celo7 Is there some mix-up of definitions going on? I would say the obvious way to define the frame "of an object" is the one where the object is always at the origin.

0celo7

I think the rest frame they're talking about is where the four-velocity is the timelike basis vector

Danu

I'm pretty sure everybody agrees on that definition.

John Rennie

We're going to get nothing done with all this kibbitzing!

barrycarter

And since it's me that's learning, that's a bad thing!

0celo7

7:17 PM

@Danu Yes, but the acceleration cannot be zero in that frame if it's not zero in other frames

Because it's tensorial

Danu

@JohnRennie You can just ignore us

@0celo7 Lol.

If an object is always at the origin, what is its acceleration?

barrycarter

I'm saying that, from my point of view, the dx of the object depends partly on t and dt in the other frame. Is that correct?

John Rennie

@Danu it's the acceleration with which an object I release accelerates away from me

barrycarter

@Danu We're talking infinitesimals here, remember?

John Rennie

Like right now my acceleration is 9.81 m/s^2

barrycarter

7:18 PM

@JohnRennie I like that. Since your own frame isn't inertial, that would sort of work.

Danu

@JohnRennie If you're releasing something, that's something different. I was just objecting against something "accelerating in its own rest frame"

@JohnRennie In your frame it's zero.

John Rennie

FFS we have language police as well as maths purists

barrycarter

@Danu As opposed to constant acceleration in the observer's frame, which leads to a paradox of sorts.

Danu

@JohnRennie In any case, I think the take-home message is: Ignore side-tracks in the conversation ;)

0celo7

@Danu Is the velocity vector $u=0$ in the rest frame?

barrycarter

7:19 PM

I probably should have done some background. I'm saying that: v du + a u du is NOT the correct dx for the remote observer.

John Rennie

@barrycarter: you can select any convenient system of coordinates and use it to calculate the four accelaration of an object e.g. me.

Danu

@0celo7 I didn't follow the conservation---I don't know what "the velocity vector" is, nor what "the rest frame" is.

John Rennie

The norm of this four-acceleration is the acceleration the observer feels in their rest frame

Danu

I also have no interest in discussing this any further---I don't think there is anything to learn here.

0celo7

@Danu You were literally just talking about the rest frame

Danu

7:20 PM

i.e. Never mind people!

0celo7

@Danu What the fuck?

barrycarter

@JohnRennie OK, I may've jumped ahead. In the object's own frame, it's position is (t,0,0,0), so its norm-like thing is -t^2, right?

Danu

@0celo7 I never said "rest frame", IIRC.

0celo7

@Danu "its frame" then

John Rennie

The problem is that the metric for the rest frame of an accelerating observer is not the Minkowski metric, it is the Rindler metric.

barrycarter

7:22 PM

@JohnRennie So I can't say the object's norm is -dt^2 in its own frame?

John Rennie

I'm abusing the terminology a bit because they are the same metric, but written in different coordinates

barrycarter

I thought ds^2 worked regardless of frame acceleration?

John Rennie

Have a look at the calculation of four acceleration for an observer in the Schwarzschild metric done here:

17

Q: What is the weight equation through general relativity?

The gravitational force on your body, called your weight, pushes you down onto the floor. $$W=mg$$ So, what is the weight equation through general relativity?

barrycarter

@JohnRennie That appears to be fairly long, so let me just ask: are you saying that in my setup, ds^2 is not constant across observers?

John Rennie

If the metric is g_\mu\nu then the norm of the four acceleration a^\mu is g_\mu\nu a^\mu a^\nu

@barrycarter ds^2 is still invariant, but you calculate ds^2 using the metric and the Earth and accelerating observer use different metrics

barrycarter

7:25 PM

@JohnRennie Er, there's no gravity involved in my problem. Just a constant acceleration object.

Slereah

Errr wait

John Rennie

@barrycarter hasn't anyone explained the equivalence principle :-)

barrycarter

@JohnRennie You're the only one who has guided me :P

John Rennie

@Slereah what have I done wrong now?

Slereah

The fancy normalization they give for momentum states is $\langle p \vert q \rangle = 2 E_p (2\pi)^3 \delta(p-q)$

Danu

7:27 PM

@JohnRennie You always do this, and I can't resist... Invariant!

John Rennie

God it's like being at school again!

Danu

(don't kill me)

Slereah

But is that normalized?

The integral over $p$ will just be $2E_q$

John Rennie

@Danu damn, and it's too late to edit now :-)

Danu

@JohnRennie Sometimes, miracles happen ;)

Slereah

7:28 PM

Shouldn't it normalize to 1

I know they are not wavefunctions stricto sensu, but still

John Rennie

@Danu how did you do that?

barrycarter

@JohnRennie I thought the entire point of using ds^2 (instead of s^2 as some other treatments do) is to allow for acceleration?

Danu

@JohnRennie I'm a moderator over at History of Science and Mathematics, which comes with network-wide moderation powers in chat...

John Rennie

@Danu Cool :-)

@barrycarter: if you want to understand relativity you need to go off and read chapter 6 of Misner, Thorne and Wheeler. I can help you work through it, but it's involved enough that I can't do it justice in this chat room.

barrycarter

@JohnRennie OK, bummer. I thought I had this down.

John Rennie

7:31 PM

Basically you can calculate the acceleration experienced by an observer from the metric.

barrycarter

Well, that's what I'm trying to do.

John Rennie

So you have to look for a metric in which the observer at the origin has a constant acceleration

barrycarter

It just gets complicated because the observer's metric must use the object's coordinates.

John Rennie

And this turns out to be the Rindler metric

barrycarter

I still think it might be do-able from the invariance of the Minkowsky metric.

You just end up solving a differential equation.

John Rennie

7:33 PM

I haven't seen it done that way, but yes I'm sure it is possible

barrycarter

OK, that's what I was going for. I wanted your help before I setup the equation.

John Rennie

I think you will save us both much pain if you read MTW first. Also check out the Physics FAQ article:

math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

for a summary of the results.

barrycarter

@JohnRennie I've read that (page, not book) many many times. I'm just trying to derive those results from first principles. I've sort of done it in some questions, but I'm looking for a clean non piecemeal derivation.

John Rennie

Maybe even check out these superbly written and easy to understand answers:

physics.stackexchange.com/search?q=rindler+user%3A1325

barrycarter

LOL :)

John Rennie

7:38 PM

@barrycarter MTW show how the equations are derived.

barrycarter

I want to try out my dfq solution first. If it works, I want to continue using the ds^2 thingy.

@JohnRennie Yes, but I'm not big into books.

And I'm ok with accepting the invariance of ds^2 as a postulate.

Slereah

Wait how do I even prove that $\langle 0 \vert a_p a^\dagger_q \vert 0 \rangle = (2\pi)^3 \delta(p-q)$

Hm

I guess since $a_p\vert 0 \rangle = 0$ I can use the commutator

John Rennie

I guess it's fun (and instructional) to do these things for yourself, but in this case I suspect the pain will outweigh the gain

0celo7

@barrycarter you can prove that

It's in Zee, probably in Carroll too

John Rennie

@barrycarter the trouble is you need the metric to compute ds^2, and you don't know the metric in the accelerating coordinates

0celo7

7:40 PM

Landau

barrycarter

Ocelot, yes, I realize you CAN prove it, but I'm saying I don't need to. I want to derive from that starting point.

Slereah

yeah nvm I got it

barrycarter

@JohnRennie For the object itself, it's always just -dt^2, right?

I have tons of time, and I love math. So, I'll try it until I get sick of it.

John Rennie

In an observer's rest frame their ds^2 = -dt^2 yes

barrycarter

@JohnRennie The trick is to find ds^2 in someone else's frame for the original observer/object.

John Rennie

7:43 PM

@barrycarter and that's what you need the metric for

barrycarter

@JohnRennie And you can't just use the obvious one.. but do you?

@JohnRennie Isn't it v[u] du + a t dt for dx?

Where v[u] is the velocity at time u

Slereah

Oh

Apparently the measure too has to be Lorentz invariant

nvm for also the previous question

John Rennie

Yes, but if you're doing the calculation in the Earth frame you need a to be the acceleration in the Earth coordinates, and that's not the same as the acceleration in the accelerating observer's coordinates

Slereah

Much like Caillou everyday I'm learning something new

barrycarter

@JohnRennie By earth frame, you mean an inertial frame, right?

John Rennie

7:45 PM

@barrycarter Yes aka the non-accelerating frame

barrycarter

@JohnRennie Correct, but notice I'm using a t dt, and NOT du. In other words, I AM using the object's coordinates.

John Rennie

You've lost me know, and in any case I need to get to bed. 6 a.m. start tomorrow (again).

barrycarter

OK, have fun :) I'll run the math and see what happens

John Rennie

Actually I think having to learn GR without a rigorous grounding in the maths forces you into understanding the physics i.e. what's actually going on. I suspect that's actually harder than working through the maths - it's certainly a prolonged and painful process.

However once you've gained an understanding, at least a partial understanding, of the physics it puts you in a superb position to answer questions from GR novices in an intuitively obvious way. I haven't check exatly what fraction of my rep comes from the GR tag, but I bet if you looked closely it was almost all due to simple ans…

Slereah

Woo

2.3 finished

Onto 2.4

Only 700 pages left

3075

8:06 PM

@Slereah I'm going to begin reading peskin and schroeder in a month so can you leave behind some stuff for me to look at kind of like what you're doing now?

like things that are unclear.

Slereah

Well ask me I guess?

It's a common thing in textbooks to not have complete proofs

barrycarter

@JohnRennie Ultimately, I believe the universe is running a mathematical equation. Using that equation, we can predict what will happen and what we will observe. However, there is no ultimate meaning behind it all. IE, physics is really nothing more than math.

3075

@Slereah yea, and thanks I will.

0celo7

I need to solve $x^{n-1}=1/\epsilon$ for $n$ and I don't know how.

:(

Slereah

Between cleaning, working out and QFT this is a Productive Week End

Use the log

0celo7

8:16 PM

Which one

Slereah

The log arithm

0celo7

Do I need

Abramowitz and Stegun

Slereah

Yes, the logarithm is some PhD level math

0celo7

@Slereah wait a moment

wait JUST one moment

Slereah

I have awaited a moment

I can't wait any longer, sorry

0celo7

8:27 PM

wait

is $\ln x^y=y\ln x$ correct

Slereah

yes

0celo7

crazy shit dude

Slereah

Did you just discover the logarithm

0celo7

yes.

@Slereah wow logs are amazing

How come we never learn about them

Slereah

I know right

Well you do, if you go to school

Man I learned about logs in high school m8

That's why the US has terrible math scores

0celo7

8:31 PM

wtf

I've never heard of a log

4

reading the wiki article right now

so interesting

Slereah

With @0celo7 I can't tell if he's trolling me

He has odd gaps in his knowledge

0celo7

have I ever trolled?

Slereah

Yes.

0celo7

wtf bro

@Slereah like what

Slereah

You have been mean to Duffield

v. inappropriate

0celo7

8:34 PM

what does Duffield have to do with anything

@yuggib These analysis proofs are fun

barrycarter

8:53 PM

Even engineers know about logs, so I think Ocelot is trolling.

0celo7

not all of us

barrycarter

Slide rules are based on logs.

0celo7

@barrycarter Maybe

barrycarter

I'm pretty sure they are.

0celo7

I love figuring out analysis problems as I'm complaining about how it's impossible to prove

3075

9:06 PM

@0celo7 5 in ap calc without a log, yeah right.

unless you forgot.

D:

barrycarter

No one forgets his first logarithm

0celo7

9:19 PM

@3075 I actually did

DanielSank

In freshman physics we consider a 1D infinite square well.

We usually consider the case where we have "one particle".

We learn that this particle can be one of various states.

For example, we suppose the particle can be in state 0, 1, 2, ... etc.

If we have multiple electrons, we say the levels get filled up from the bottom upward, with one electron per level.

What happens if we fill the thing with bosons?

0celo7

9:38 PM

what are you talking about

you did QM in freshman physics?

Slereah

9:53 PM

I did some QM in the last year of high school

It was pretty lowkey, though

Just like "hydrogen has discrete levels, compute some energy for transitions"

user507974

guys, how goes it

MonaLisaOverdrive

11:13 PM

Hello all…

Has anyone here read Quantum Mechanics: The Theoretical Minimum?

I'm beginning to suspect that understanding the mathematical concepts described within may require a solid understanding of linear algebra…

…and I'm hoping to confirm

Went back and skimmed intro…book requires basic knowledge of linear algebra. Unfortunately when I originally bought the book I thought that linear algebra = high-school algebra.

MonaLisaOverdrive

11:43 PM

/me heads off to purchase linear algebra for dummies

user507974

@MonaLisaOverdrive linear algebra is like the god of math for physicists

get very good with linear algebra

MonaLisaOverdrive

I was afraid you'd say that.

user507974

@MonaLisaOverdrive get VERY good

you need not be afraid youngling

MonaLisaOverdrive

I find your use of the term 'youngling' amusing

user507974

linear algebra kinda is really 5 or 6 concepts repeated again in a million ways to make you understand how universal it is

MonaLisaOverdrive

11:47 PM

So…if I get a good understanding of the 5 or 6 concepts, I can re-tackle The Theoretical Minimum?

'Cause my time is rather…restricted

user507974

im not probably really doing it justice, but basically what you do is identify what the concept of a vector space is, its a first real dive into the structure of math

and getting good with understanding linear algebra will save you time all the way through the rest of your physics learning

so give it some real attention, since basically most of the things you will do with physics have analogs in linear algebra notation,

Hey @ACuriousMind is there anything this article is actually getting wrong about the holographic universe models motherboard.vice.com/read/…

MonaLisaOverdrive

Welp…back to the drawing board.

user507974

@MonaLisaOverdrive you know how currently energy conservation seems like something really important to you

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